Reduced-order state reconstruction for nonlinear dynamical systems in the presence of model uncertainty

A new approach to the reduced-order state reconstruction problem for nonlinear dynamical systems in the presence of model uncertainty is proposed. The problem of interest is conveniently formulated and addressed within the context of singular first-order non-homogeneous partial differential equations (PDE) theory, leading to a reduced-order nonlinear state estimator that is constructed through the solution of a system of singular PDEs. A set of necessary and sufficient conditions is derived that ensure the existence and uniqueness of a locally analytic solution to the above system of PDEs, and a series solution method is developed that is easily programmable with the aid of a symbolic software package such as MAPLE. Furthermore, the convergence of the estimation error or the mismatch between the actual unmeasurable states and their estimates is analyzed and characterized in the presence of model uncertainty. Finally, the performance of the proposed reduced-order state reconstruction method is evaluated in a case study involving a biological reactor that exhibits nonlinear dynamic behavior.